Here is what I get for the first one. A(3,3)
Obviously the answer is wrong, but all the steps up to the answer should be correct.
So I can calculate the answer myself from the last step, which is 4 I think.

1 Attachment

That works fine, now the problem is when I try A(3, 4) although I get the answer to be 0, it outputs for about 30 seconds, so I get like 1000s of lines of output which would be a bit too much to write. lol.
Anyway, I'm thinking there must be some way to recognize a pattern in order to get the answer. :/

A(3,4)
=A(2,A(3,3))
=A(2,2^16)
=A(1,A(2,2^16-1))
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Let's look at A(2,2^16-1)
A(2,2^16-1)=A(1,A(2,2^16-2))
There is like a pattern going on we have
A(2,2^16-b) b keeps increasing eventually it will get to 2^16
Since this is happening in the n part of A then the output will be 0.

@myininaya
Hi there, could you look over this one more time. According to my teacher, it is impossible to find the second number for A(3,4) by using a computer algorithm. And the students in my class are saying the answer is a really big number and not 0. Like a lot bigger then the number for A(3,3)
Do you have any idea where that would be coming from?

The teacher hasn't looked at my work yet, he was just giving hints to help with the homework, and he said that this part cannot be done with a computer program because it will run out of memory and lose the answer.

No, the teacher didn't say anything about the answer, just that it couldn't be done with a computer, and since I got the same number with I computer 0, as you got by hand, I figured it couldn't be right unless my teacher was wrong.